Since a quantum computer uses the state of quantum mechanical superposition, decoherence by which this state breaks causes a memory error or gate error. This is a problem that is unique to the quantum computer and does not arise in the conventional classical computers. Therefore, quantum error correction capable of correcting an error like this and fault-tolerant quantum computation that performs reliable quantum computation by using the quantum error correction are regarded as indispensable in the quantum computer.
Theoretically, reliable quantum computation can be executed as long as possible if the error probability is lower than a certain threshold (the threshold theorem). The threshold depends on the method of fault-tolerant quantum computation, and the present highest value is still low, i.e., about 1%. In addition, even when the threshold is 1%, the resources (the qubit count and (or) the gate count) become enormous. Therefore, demands have arisen for a better fault-tolerant quantum computation method.
Classical error correction has dramatically improved the performance by changing algebraic hard-decision decoding to soft-decision decoding based on probabilistic inference. Accordingly, it may be possible to improve the performance of fault-tolerant quantum computation by soft-decision decoding. Note that there is a related art of quantum error correction using soft-decision decoding based on probabilistic inference.
Unfortunately, fault-tolerant quantum computation using soft-decision decoding has not been studied yet, and its performance is unknown.